Question

if alpha and beta are the zeros of the polynomial P(x) is = 2 x square - 8 x + a minus b such that (alpha + 1 )(beta + 1) is equal to zero then find the value of b

Answer 1

you did mistake something here,
becoz for finding value of b one more relation require ,
here, (a - b) = -10

alpha ànd beta are the zeros of
P(x ) = 2x² - 8x + (a - b)
so,
sum of zeros ( alpha + beta ) = -(coefficient of x)/coefficient of x² = -(-8)/2 = 4

products of zeros ( alpha.beta ) = constant/coefficient of x² = ( a - b)/2

given ,
(alpha + 1)(beta + 1) = 0
alpha.beta + ( alpha + beta )+ 1 = 0
put above results ,
(a - b)/2 + 4 + 1 = 0

(a - b) = -10

now, polynomial P(x ) = 2x² -8x -10
{ put (a - b) = -10 }

2x² - 8x - 10

= 2x² - 10x + 2x -10

= 2x (x -5) +2(x -5)

=(2x +2)(x -5)

hence, x = -1 and 5 are zeros of given polynomial P(x )

Answer 2

Hi there !!

p(x) = 2x² - 8x + a - b



α + β = -b/a = 8/2 = 4
αβ = a-b / 2

α and β are zeros of p(x)


Given :-

(α + 1) (β + 1 ) = 0
αβ + (α + β) + 1 = 0
a-b/2 + 4 + 1 = 0

a-b/2 + 5 = 0

a-b/2 + 10/2 = 0

[a-b+10]/2 = 0

a-b + 10 = 0

a- b = -10

Hence ,
the polynomial should be :-

p(x) = 2x²- 8x + 10 

We cant find the value of "b"

one more relation is required .

I'm just finding the zeros of p(x)


2x² - 10x + 2x -10 

= 2x (x -5) + 2(x -5) 

=(2x +2) (x -5) 



x = -2/2 = -1
x = 5

zeros are -1 and 5